Wave scattering by a circular cylinder half-immersed in water with an ice-cover (original) (raw)
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Water wave scattering by a nearly circular cylinder submerged beneath an ice-cover
Journal of Marine Science and Application, 2015
Assuming linear theory, the two-dimensional problem of water wave scattering by a horizontal nearly circular cylinder submerged in infinitely deep water with an ice cover modeled as a thin-elastic plate floating on water, is investigated here. The cross-section of the nearly circular cylinder is taken as r=a(1+δC(θ)), where a is the radius of the corresponding circular cross-section of the cylinder, δ is a measure of small departure of the cross-section of the cylinder from its circularity and C(θ) is the shape function. Using a simplified perturbation technique the problem is reduced to two independent boundary value problems up to first order in δ. The first one corresponds to water wave scattering by a circular cylinder submerged in water with an ice-cover, while the second problem describes wave radiation by a submerged circular cylinder and involves first order correction to the reflection and transmission coefficients. The corrections are obtained in terms of integrals involving the shape function. Assuming a general Fourier expansion of the shape function, these corrections are evaluated approximately. It is well known that normally incident wave trains experience no reflection by a circular cylinder submerged in infinitely deep water with an ice cover. It is shown here that the reflection coefficient also vanishes up to first order for some particular choice of the shape function representing a nearly circular cylinder. For these cases, full transmission occurs, only change is in its phase which is depicted graphically against the wave number in a number of figures and appropriate conclusions are drawn.
Oblique wave scattering by a circular cylinder submerged beneath an ice-cover
International Journal of Engineering Science, 2006
When a train of small-amplitude surface water waves is normally incident on a very long horizontal circular cylinder fully submerged in deep water with a free surface, it is well known that it passes over and below the cylinder with a change of phase without experiencing any reflection. However the cylinder does experience reflection for oblique incidence of the surface wave train. It is shown here that the same phenomenon also holds good when the deep water has an ice-cover instead of a free surface, the ice-cover being modelled as a thin elastic plate. Here, for oblique incidence, the reflection and transmission coefficients are obtained approximately and depicted graphically against the wave number in a number of figures.
Wave scattering by a horizontal circular cylinder in a two-layer fluid with an ice-cover
International Journal of Engineering Science, 2007
In a two-layer fluid wherein the upper layer is of finite depth and bounded above by a thin but uniform layer of icecover modelled as a thin elastic sheet and the lower layer is infinitely deep below the interface, time-harmonic waves with a given frequency can propagate with two different wavenumbers. The wave of smaller wavenumber propagates along the ice-cover while wave of higher wavenumber propagates along the interface. In this paper problems of wave scattering by a horizontal circular cylinder submerged in either the lower or in the upper layer due to obliquely as well as normally incident wave trains of both the wave numbers are investigated by using the method of multipole expansions. The effect of the presence of ice-cover on the various reflection and transmission coefficients due to incident waves at the ice-cover and the interface is depicted graphically in a number of figures.
Scattering of water waves by thin vertical plate submerged below ice-cover surface
Applied Mathematics and Mechanics-english Edition, 2011
The present paper is concerned with scattering of water waves from a vertical plate, modeled as an elastic plate, submerged in deep water covered with a thin uniform sheet of ice. The problem is formulated in terms of a hypersingular integral equation by a suitable application of Green's integral theorem in terms of difference of potential functions across the barrier. This integral equation is solved by a collocation method using a finite series involving Chebyshev polynomials. Reflection and transmission coefficients are obtained numerically and presented graphically for various values of the wave number and ice-cover parameter.
Wave scattering by a thin vertical barrier submerged beneath an ice-cover in deep water
Applied Ocean Research, 2010
The two-dimensional problem of water wave scattering by a thin inclined semi-infinite rigid barrier submerged in infinitely deep water covered by a thin uniform ice sheet modelled as an elastic plate, is investigated here. It is formulated in terms of a hypersingular integral equation for the discontinuity of the potential function across the barrier. The integral equation is solved numerically by approximating the discontinuity by a finite series involving Chebyshev polynomials of second kind multiplied by an appropriate weight function. The reflection and transmission coefficients are obtained approximately and their numerical estimates for the vertical barrier for different values of the ice-cover parameters and the wave number are found. In the absence of the ice-cover, known results for a free surface are recovered. The reflection and transmission coefficients for the vertical barrier are depicted graphically against the wave number for various values of the ice-cover parameters.
2013
for the 29th Intl Workshop on Water Waves and Floating Bodies, Osaka (Japan), March 30 –April 02, 2014 Radiation of Waves by a Cylinder Submerged in the Fluid beneath an Elastic Ice Sheet with a Partially Frozen Crack by I.V. Sturova Lavrentyev Institute of Hydrodynamics of SB RAS, pr. Lavrentyeva 15, Novosibirsk, 630090, Russia E-mail: sturova@hydro.nsc.ru Highlights: • Using the method of matched eigenfunction expansions for the velocity potentials, the mathematical problem is handled for solution. • Reciprocity relations are newly found which relate the damping coefficients of the submerged body to the far-field form of the radiation potentials.
Scattering of water waves by thick rectangular barriers in presence of ice cover
Journal of Ocean Engineering and Science, 2020
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Water wave scattering by a submerged circular-arc-shaped plate
Fluid dynamics research, 2002
The problem of water wave scattering by a thin circular-arc-shaped plate submerged in infinitely deep water is investigated by linear theory. The circular-arc is not necessarily symmetric about the vertical through its center. The problem is formulated in terms of a hypersingular ...
On underwater sound reflection from layered ice sheets
2016
Reflection of sound from ice sheets floating on water is simulated using Thomson and Haskell's method of matrix propagation. The reflection coefficient is computed as a function of incidence angle and frequency for selected ice parameters of a uniform sheet and two layered ice sheets. At some incidence angles and frequencies the reflection coefficient has very low values. It is shown that this is related to generation of Lamb waves in the ice. The matrix propagation method also provides a dispersion equation for a plate loaded with fluid on one side and vacuum on the other. Finally the concept of beam displacement is briefly discussed.
Scattering of water waves by a submerged thin vertical elastic plate
Archive of Applied Mechanics, 2013
The problem of water wave scattering by a thin vertical elastic plate submerged in infinitely deep water is investigated here assuming linear theory. The boundary condition on the elastic plate is derived from the Bernoulli-Euler equation of motion satisfied by the plate. This is converted into the condition that the normal velocity of the plate is prescribed in terms of an integral involving the difference in velocity potentials (unknown) across the plate multiplied by an appropriate Green's function. The reflection and transmission coefficients are obtained in terms of integrals involving combinations of the unknown velocity potential on the two sides of the plate and its normal derivative on the plate, which satisfy three simultaneous integral equations, solved numerically. These coefficients are computed numerically for various values of different parameters and are depicted graphically against the wave number for different situations. The energy identity relating these coefficients is also derived analytically by employing Green's integral theorem. Results for a rigid plate are recovered when the parameters characterizing the elastic plate are chosen negligibly small.